Simplify the radical 189 3 \sqrt [ 3 ] { 189 } 3 189 , if possible.A) 3 7 3 3 \sqrt [ 3 ] { 7 } 3 3 7 B) 3 21 3 \sqrt { 21 } 3 21 C) 3D) 10 3 10 \sqrt { 3 } 10 3 E) 6 7 3 6 \sqrt [ 3 ] { 7 } 6 3 7

Question

Simplify the radical   189 3 \sqrt [ 3 ] { 189 } 3 189 ​   , if possible.A)    3 7 3 3 \sqrt [ 3 ] { 7 } 3 3 7 ​ B)    3 21 3 \sqrt { 21 } 3 21 ​ C) 3D)    10 3 10 \sqrt { 3 } 10 3 ​ E)    6 7 3 6 \sqrt [ 3 ] { 7 } 6 3 7 ​

Latheresa Kemper · Accepted Answer

Final Answer : A, Explanation :   To simplify   189 3 \sqrt[3]{189} 3 189 ​  , factor 189 into prime factors:   189 = 3 3 × 7 189 = 3^3 	imes 7 189 = 3 3 × 7  . Thus,   189 3 = 3 3 × 7 3 = 3 7 3 \sqrt[3]{189} = \sqrt[3]{3^3 	imes 7} = 3\sqrt[3]{7} 3 189 ​ = 3 3 3 × 7 ​ = 3 3 7 ​  .

Simplify the radical $1893\sqrt [ 3 ] { 189 }$ , if possible.

A) $\sqrt [ 3 ] { 7 }$
B) $\sqrt { 21 }$
C) 3
D) $\sqrt { 3 }$
E) $\sqrt [ 3 ] { 7 }$

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Related questions

Simplify the radical 1893\sqrt [ 3 ] { 189 }3189​ , if possible.A) 3733 \sqrt [ 3 ] { 7 }337​ B) 3213 \sqrt { 21 }321​ C) 3D) 10310 \sqrt { 3 }103​ E) 6736 \sqrt [ 3 ] { 7 }637​

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Learning Objectives

Learning Objectives

Related questions

Simplify the radical $1893\sqrt [ 3 ] { 189 }$ , if possible.

A) $\sqrt [ 3 ] { 7 }$
B) $\sqrt { 21 }$
C) 3
D) $\sqrt { 3 }$
E) $\sqrt [ 3 ] { 7 }$